# Difference between revisions of "Direct space"

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== Other languages == | == Other languages == | ||

− | Espace direct (''Fr''). Direktes Raum (''Ge''). Espacio directo (''Sp''). | + | Espace direct (''Fr''). Direktes Raum (''Ge''). Espacio directo (''Sp'').<Font color="black"> Spazio diretto </Font>(''It'') |

== Definition == | == Definition == |

## Revision as of 15:28, 17 March 2006

## Other languages

Espace direct (*Fr*). Direktes Raum (*Ge*). Espacio directo (*Sp*). Spazio diretto (*It*)

## Definition

The direct space (or *crystal space*) is the *point space*, *E ^{n}*, in which the structures of finite real
crystals are idealized as infinite perfect three-dimensional structures. To this space one associates the

*vector space*,

*V*, of which lattice and translation vectors are elements. It is a

^{n}*Euclidean*space where the scalar product of two vectors is defined. The two spaces are connected through the following relations:

(i) To any two points *P* and *Q* of the point space *E ^{n}* a vector

**PQ**=

**r**of the vector space

*V*is attached

^{n}(ii) For each point *P* of *E ^{n}* and for each vector

**r**of

*V*there is exactly one point

^{n}*Q*of

*E*for which

^{n}**PQ**=

**r**holds

(iii) If *R* is a third point of the point space, **PQ** + **QR** = **PR**

## See also

direct lattice

Section 8.1 of *International Tables of Crystallography, Volume A*